A complete tree, also known as a full binary tree, is a special type of binary tree in data structure. In a complete tree, all levels are completely filled except possibly for the last level, which is filled from left to right.
Properties of a Complete Tree
A complete tree has the following properties:
- Fullness: Every level except the last level is completely filled with nodes.
- Left Alignment: Nodes in the last level are left-aligned.
Examples of Complete Trees
Let’s take a look at some examples to understand complete trees better.
In this example, we have a complete tree with four levels. All levels are completely filled except for the last level.
A / \ B C / \ D E
In this example, nodes A, B, C, and D are present in all levels. However, node E is only present in the first and second levels. Since all levels except the last are completely filled, this tree is considered a complete tree.
In this example, we have a complete tree with three levels. All levels are completely filled.
A / \ B C / \ / \ D E F G
In this example, all levels of the tree are completely filled. Therefore, it satisfies the property of being a complete tree.
Applications of Complete Trees
Complete trees have various applications in computer science and data structures:
- Heap Data Structure: Complete trees are used to implement heaps, which are binary trees with special properties used in priority queues and sorting algorithms like heap sort.
- Binary Tree Representation: Complete trees are used to represent binary trees compactly using arrays or lists.
A complete tree is a special type of binary tree where all levels except the last are completely filled. It has various applications in data structures and algorithms. Understanding complete trees is essential for efficient implementation of related concepts.
In this article, we explored the properties of complete trees, provided examples for better understanding, discussed their applications, and emphasized the importance of understanding this concept in data structures.